Logarithm Curriculum Refresh Continued
We have been doing logarithms for exactly one week now, and overall I am happy with the restructured curriculum that I have been working on. There are a couple things I will change for next year to make it more seamless, but my goal has been to change up the order of things to really emphasize the conceptual idea of WHAT a logarithm is and to use this when solving to avoid common errors. I also restructured the properties of logarithms to allow students to discover them on their own.
Here is what I have done so far since my last blog post on Logarithms:
After building up the idea that a logarithm is just an exponent and then playing Logarithm War to practice mentally evaluating, students watched my two videos on EdPuzzle (VIDEO LINKS HERE and HERE).
These videos showed them how to convert from exponential to logarithmic form and back, told them the two types of logarithms, showed them how to do change of base on a calculator to evaluate any logarithm, and how to solve basic exponential equations by converting to logarithmic form.
The next class, we spent about half an hour doing whiteboard practice of solving exponential equations by converting to logarithmic form. These equations started off very simple and slowly increased in difficulty - but by the end, they were still just barely intermediate level. This was essentially thin-slicing practice, but because I knew they would finish each problem so quickly, I didn’t have them complete these at the VNPS (I would’ve been running around like crazy and would have never caught up!). Instead, they did these on 1 ft x 1 ft individual whiteboards at the same time.
Sidenote: these “whiteboards” are the low-cost Lowes hardboard panels that a store employee cut up for me eleven years ago! They are still being used (although a bit worse for wear), and were absolutely worth buying!
After each question, I showed my done-out solution for them to compare and then I put up a new question. Problems here:
They did really well with these problems and felt confident.
Instead of moving to the inverse property of logarithms and how we can use it to solve logarithmic and exponential functions, I decided to have them discover the Properties of Logarithms next. I based this off of the NCTM activity “Demystifying Logarithms” and I love it. I had never thought of having them discover these three properties numerically in groups until this month when I saw NCTM’s activity. Here is my FILE of student handout.
After making sure they had the three properties written down from that activity, I incorrectly thought that they would be able to move right into expanding and then condensing logarithms. WRONG! This is something to fix for next year! I handed out a newly typed worksheet on expanding logarithms first, but they were overall confused and not sure what the main goal was or how to tell if you were fully expanded. Before I had time to address their questions, the bell rang, so I made a game-time decision and had them watch a video on EdPuzzle I had made previously on Expanding and Condensing Logarithms (Video LINK HERE). I was hoping the Demystifying Logarithms discovery activity would have avoided needed this video, but they really benefitted from seeing some examples done out and explained to really get a grasp on how to handle radicals, exponents, when to stop, etc.
Here is my PDF FILE on expanding and condensing logarithms. I still love these problems and the way they increase in complexity, I just need to better clarify beforehand how to do these.
Also, to see the power of nicely laying out and formatting worksheets and problem sets that you create yourself, take a look at how much nicer this worksheet looks when in a table format! I was about to make copies of the first version, but decided to put the problems in a table to help them stay organized. Also, NUMBERING! Numbering helps SO MUCH when going over problems so students can easily refer to a problem they have a question on.
Today, students used their new knowledge on the properties of logarithms to solve more complex logarithmic equations. They did these at the VNPS in random pairs. PDF file HERE of the thin-sliced questions. Some of them were thinking so much about condensing that they completely forgot where to go next, so I had to remind them about converting out of logarithmic form.
Their homework this weekend is to watch a video I made on EdPuzzle on Inverse Functions and how they relate to Exponential and Logarithmic Functions. We will spend Monday at the VNPS finishing today’s “condense logs and solve” thin-sliced problems followed by questions on graphing and shifting logarithms on the large graph whiteboard.
Here is a cool article I found on how logarithms relate to Reddit upvotes and downvotes. I’m not sure if it will be beyond what my students can understand/care about, but HERE it is for my future reference!